There's much structure in the ENSO model phase plots
By multiplying the points by the strength of the annular impulse at that time, the phase-plots give away the source of the alignment
Leading month pulse:
Trailing month pulse:
There's also a 3-D quality to these plots, akin to a skewed perspective view of a box. This exercise is essentially one of extracting a geometric order out of once was a seemingly erratic time-series.
The erratic translation of the squared contours is due to a square wave that's staggered by a primary tidal cycle which is incommensurate with the annual impulse. IOW, if the sine wave and the annual impulse were the same period, a lagged impulse response would create a perfect square wave, not one that looks like this